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* *Reflection: Diverse Entry Points
Going Graphic - Section 3: Wrap it Up

This student sample uses one of the graphic organizers I keep available for all my classes. I've found that each student has his/her preferences when it comes to organizing information, so I usually don't require a specific format but allow them to decide how to respond. I chose this example because the student did a nice job of succinctly comparing and contrasting. This kind of exit ticket can be tough to grade if you focus on whether or not a student responds as you expect them to, but I try to be flexible and instead focus on whether or not each student expresses an understanding of the content in question. I make note of those who don't seem to have that understanding and also of those who use more unconventional ways to respond. Students in the first group will probably need additional support as we move forward and students in the second group may become more easily frustrated by traditional presentations of mathematics as are often seen on standardized exams.

# Going Graphic

Lesson 4 of 10

## Objective: SWBAT create and graph complicated equations, using the graphs to predict and/or solve for given values.

## Big Idea: Try this lesson to energize graphing skills and understanding by giving students practice with real-world connections.

*55 minutes*

#### Set the Stage

*10 min*

I begin this lesson with the height vs shoe size equation from yesterday's lesson on the board. An example would look like "*y = 0.4x - 14*". I ask my students to pair-share what they think it would look like as a graph and why? After a few minutes I randomly select students to share what they talked about and sketch their ideas on the front board. **(MP4)** Since they also need to explain why they think the graph will look like that I get a quick assessment of my students' understanding of graphing.

I leave the sketches posted, give each student a sheet of graph paper, and ask them to graph the equation. I remind them that x represents height in inches and y represents shoe size. I stay with x and y for now, but may be able to switch to f(x) and x when more of my students are familiarized with those terms in earlier classes. I also tell them that their graphs should have the axes and scales labeled. **(MP6)** When everyone is finished I ask them to compare what they've graphed to the sketches and congratulate themselves if their sketches were close to being correct. I then ask them to use their graph to predict the shoe size of someone who is 58 inches tall. Some students will say that it's not possible because they didn't make their graph big enough. I commiserate and suggest that our work yesterday included people as tall as 76 inches and as short as 28 inches, and that because the data is for human heights and shoe sizes that should have given them an idea of how to set up the scales for their graph. I then repeat my question about predicting the shoe size of someone 58 inches tall let volunteers give their best estimates. I finish by saying that scientists did similar calculations and used paper and pencil graphs to build the Eiffel Tower and to put men on the moon.

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#### Put it into Action

*40 min*

*You will need copies of the Graphing Problems for this section of the lesson. * I tell my students that now that we've worked through the toy story example as a group they will be working independently to solve two-variable problems by graphing them manually. I say that labels are important and that precision will make their work much easier. I remind them that they are welcome to use the rulers and graph paper I have and ask that they not crowd their graphs but also don't spread them to fill the page unless necessary. I distribute the Graphing Problems and ask if there are any questions. **(MP1, MP2, MP4)** While my students are working I walk around offering encouragement and redirection as needed. For example, I a student is struggling to come up with a model I might suggest that they estimate a few data points to get an idea of the shape of the graph.

When everyone is done I tell them that they will be self-checking their papers so that they have a reference for graphing when they need it. I project each problem on the board using my document camera and projector so my students can see the graphs as well as the points I estimated.

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#### Wrap it Up

*5 min*

To close this lesson I ask my students to compare, in writing, making predictions from a graph as they did today and using an equation like they did yesterday. I explain that I don't just want to know which one they think is easier or faster, I want to know the strengths and weaknesses of each method. If you'd like sample questions to guide this reflection you might try these:

- What was the easiest thing about predicting from an equation? Why?
- What was the hardest thing about predicting from an equation? Why?
- What was the easiest thing about predicting from an graph? Why?
- What was the hardest thing about predicting from an graph? Why?
- Using your answers to questions 1-4, briefly compare the strengths and weaknesses of making predictions from an equation or a graph.

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review

- LESSON 1: Make It
- LESSON 2: Make it More
- LESSON 3: Double Trouble
- LESSON 4: Going Graphic
- LESSON 5: Out of Bounds
- LESSON 6: Limiting Your Options
- LESSON 7: Does it Work?
- LESSON 8: Twist It
- LESSON 9: Creating Algebraically Review Stations
- LESSON 10: Creating Algebraically; Assessment